Estimation of maximum potential losses for digital banking transaction risks using the extreme value-at-risks method

Saputra, Moch Panji Agung; Sukono; Chaerani, Diah Article Estimation of maximum potential losses for digital banking transaction risks using the extreme value-at-risks method Risks Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Saputra, Moch Panji Agung; Sukono; Chaerani, Diah (2022) : Estimation of maximum potential losses for digital banking transaction risks using the extreme value-at-risks method, Risks, ISSN 2227-9091, MDPI, Basel, Vol. 10, Iss. 1, pp. 1-18, https://doi.org/10.3390/risks10010010 This Version is available at: https://hdl.handle.net/10419/258321 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Risks 10: 10. https://doi.org/10.3390/risks 10010010 Academic Editor: Mogens Steffensen Received: 30 October 2021 Accepted: 17 December 2021 Published: 3 January 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). risks Article Estimation of Maximum Potential Losses for Digital Banking Transaction Risks Using the Extreme Value-at-Risks Method Moch Panji Agung Saputra 1,* , Sukono 2and Diah Chaerani 2 1Master of Mathematics Study Program, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia 2Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Indonesia; [email protected] (S.); [email protected] (D.C.) *Correspondence: [email protected]; Tel.: +62-898-7058-643 Abstract: The application of industry 4.0 in banking presents many challenges, with several operational risks related to downtime and timeout services due to system failures. One of the operational risk management steps is to estimate the value of the maximum potential losses. The purpose of this study is to estimate the maximum potential losses for digital banking transaction risks. The method used for estimating risks is the EVaR method. There are several steps in this study. The first step is to resample the data using MEBoot. This process is a simulation of the operational risk loss data of digital banking. Next, the threshold value is determined to obtain the extreme data value. Then, a Kolmogorov–Smirnov test is conducted to fit the data with the GPD. Afterward, the GPD parameter is estimated. Then, EVaR is calculated using a portfolio approach to obtain a combination of risk values as maximum potential losses. The analysis results show that the maximum potential loss is IDR144,357,528,750.94. The research results imply that the banks need to pay attention to the maximum potential losses of digital financial transactions as a reference for risk management. Therefore, banks can anticipate the adequacy of reserve funds for these potential risks. Keywords: digital banking; digital transaction system risks; risk management; maximum potential losses; EVaR method; portfolio approach 1. Introduction Industry 4.0 refers to the concept that technology has permeated all areas of society: production, finance, services, transportation, and communications (Cividino et al. 2019). The current global economy is constantly changing so that innovation and technological development are key issues in a sustainable approach. Industry 4.0 in banking system technologies is applied in digitizing assets, creating a digital identity, providing special offers to customers, and offering customization (Nethravathi et al. 2020). Financial service providers are not only banks but also other financial institutions such as non-bank FinTech. Banking companies need to ensure that they keep up and take significant steps to compete effectively with financial institutions at the forefront of technology, such as FinTech and WealthTech companies. The introduction of next-generation technologies, such as application programming interfaces (API), artificial intelligence (AI), machine learning, and robotics, is demanded to bring the customer experience to a new level of convenience (Mishra 2020;Carbo-Valverde et al. 2020a). In this case, the focus is bank companies because the reach of customers from banking companies is greater than non-banks. In addition, financial transaction services offered by banks can be more comprehensive than non-banks. Therefore, banking companies must be able to develop digital technology to increase the advantages of financial transaction activities (Carbo-Valverde et al. 2020b). The development of new digital information technology in banking has a positive effect on financial activities in banks (Rahman et al. 2018). The main positive impact is to make transactions easier for customers. Customers do not need to make financial Risks 2022,10, 10. https://doi.org/10.3390/risks10010010 https://www.mdpi.com/journal/risks Risks 2022,10, 10 2 of 18 transactions at the bank but only use their gadgets. This is also a good impact on postCOVID-19 life because digital banking has reduced direct interaction. The digital or electronic banking services include: (a) account statements for customers; (b) information on banking products (deposits, loans, securities); (c) applications for opening deposits and obtaining loans and bank cards; (d) internal transfers to bank accounts; (e) transfers to an account at another bank; (f) currency conversion; (g) bill payments; (h) online shopping payment instruments; (i) topping up e-money or e-wallets; (j) and a means of payment in conventional stores using a QR code (Susanto et al. 2016;Hernández-Murillo et al. 2010). The first two types of services can be carried out using only cellular communication. Still, an Internet connection is usually required for the other services. With various digital services for customers to facilitate financial transactions, banking companies compete with FinTech or WealthTech. Banking companies must be able to provide a wider range of digital services so that customers are more interested in using banking services and the value of banking transactions will increase. Referring to the report of the Institute of International Finance, data digitization activities and bank financial operations also create around 70% of the digital risk for banks. The report also shows that 22% of banks worldwide have invested more than 25% of their annual budgets in digitizing risk management (Institute of International Finance 2017). The risk of digital financial transaction activities in a bank can be generalized by several indicators such as (a) risk of defects and system failure; (b) risk of losing data integrity and unauthorized access to customer data; (c) risk of the violation of technical systems in an information room; (d) risk of cyber-attack; and (e) risk of misuse of the system (Zabala Aguayo and ´ Slusarczyk 2020;Casalóet al. 2007;Ojeniyi et al. 2019;Sarma and Singh 2010). Banking companies need to pay attention to the existence of risks related to digital financial transactions. Besides taking advantage of these new opportunities, banks must identify, measure, monitor, and control these risks with prudent principles (Tanase and Serbu 2010). Based on the regulations of the Indonesian Financial Services Authority (OJK) number 7/POJK.03/2016 and the provisions of Law 2/No.10/1998, it is stated that Indonesian banks, in conducting their business, are based on economic democracy by using the principle of prudence. Because digital financial activities pose an increased risk, banks are required to apply prudential principles and risk management. As a consequence, one form of regulatory implementation is the real-time gross settlement (RTGS) system to minimize the risks of digital financial transactions (Iman 2020;Lubis et al. 2019). RTGS is implemented if there is a system failure during a transaction, in which case bank companies are required to send new transactions in real time. The new transaction must be executed immediately without waiting for a refund. The funds used in the new transaction are the bank’s own company funds. This makes it important to allocate reserve funds for operational risks (Keister and McAndrews 2009;Belás et al. 2016). Related to the operational risks and the need to measure the reserve fund allocation, it is necessary to calculate the maximum potential losses. The method used to calculate the maximum potential losses is value-at-risk (VaR), with extreme value theory (EVT) for extreme risks. In economics and finance, the risk of loss can be measured using VaR. If the economic phenomenon shows an extreme event, an EVT approach is needed to represent it. VaR is the maximum loss that will not be passed for a probability defined as the confidence level over a certain time (Esterhuysen et al. 2008). Securities institutions or banks usually use VaR to measure the risk of their asset portfolio or the company’s operational risk (Boudt et al. 2013;Aebi et al. 2012). The VaR analyzed by EVT can be called extreme value-at-risk (EVaR) (Muteba Mwamba and Mhlanga 2013). If more than one risk is analyzed, the EVaR needs to be measured with a portfolio approach to obtain a combination of risks based on the weight of each risk. Therefore, the EVaR obtained is a weighted result that represents each risk (Gilli and Këllezi 2006). One study that carried out the calculation or modeling of bank reserve funds was conducted by Schalkwyk and Witbooi (van Schalkwyk and Witbooi 2017), who considered the spread model of bank reserves to cover the maximum potential Risks 2022,10, 10 3 of 18 loss due to banking risks. They formulated optimal stochastic control problems related to minimizing the risk of deposits and the reserve process, net cash flow from storage activity, and the cumulative costs of the bank’s strategic sector. Several relevant studies on the problem of EVT and EVaR analysis and its relationship to banking have been conducted. Abbate et al. (2009) conducted data modeling with big data tails using EVT and introduced the copula theory. They showed that VaR with EVT becomes the measurement of the risk that occurs. In addition, the results show that the use of standard VaR is not appropriate for risk asset diversification involving a mean-infinite distribution (representing extreme events). Therefore, the EVT approach is needed to determine VaR in extreme events. Baran and Witzany (2011) conducted a study comparing EVT with standardized estimation methods (variance, covariance, historical simulations) to produce value-at-risk. This value-at-risk search method is compared with backtesting procedures and produces variated volatility returns in a given period of time. Gilli and Këllezi (2006) applied the EVT to measure risk. EVT is considered to provide the basis for extreme statistical modeling. Many science and modern engineering fields must deal with rare events that have significant consequences and are usually called extreme events. That study was intended to explain the basics of EVT and the tactical aspects of predicting and evaluating the statistical models for measuring risk from extreme incidents. Furthermore, risk measures for the banking sector have been discussed in several studies. Esterhuysen et al. (2008) performed EVaR management in financial institutions through robust calculation techniques and the effect of this value on the capital owned by the bank for operational risk. The robust calculation, among others, collected the operational loss data, then tracked operational loss data and used a robust internal risk control system. They illustrated the differences of an internal risk control system in regulatory capital when using the advanced measurement approach (AMA) and the standardized approach (SA) by using examples of banking problems. Yao et al. (2013) observed that operational risk management plays an important role in decision making for banks. The conditional value-at-risk (CVaR) model based on the peak value method from the EVT analysis is used to measure operational risk. Bank loss data are used with empirical analyses. Tests are conducted using the EVaR and CVaR EVT calculation models at 95% and 99% confidence levels, respectively, to assess expected and unexpected losses in operational risk. After conducting the literature review, the study suggested the gaps between the previous and present studies, as summarized in Table 1. Table 1. Research gap. Authors Titles Methods Risks (Variables) Gilli and Këllezi (2006) An Application of Extreme Value Theory for Measuring Financial Risk Extreme value theory, value-at-risk, expected shortfall Market risk, financial series, daily returns of some financial portfolios Esterhuysen et al. (2008)Calculating Operational Value-at-Risk in a Retail Bank Operational value-at-risk, advanced measurement approach, standardized approach Operational losses data in the retail bank, gross income, net interest income Yao et al. (2013) CVaR Measurement and Operational Risk Management in Commercial Banks According to the Peak Value Method of the Extreme Value Theory Conditional value-at-risk, peak value method, extreme value theory Operational risks, losses data of commercial banks van Schalkwyk and Witbooi (2017) A Model for Bank Reserves Versus Treasuries under Basel III Portfolio diversification, stochastic optimal control Deposit risk, cumulative cost, net cash flows in a bank This work The Estimation of Maximum Potential Losses of Digital Banking Transactions Risks Using the Extreme Value-at-Risks Method Extreme value-at-risk, portfolio approach Operational risks, digital banking transactions risks Risks 2022,10, 10 4 of 18 Based on Table 1, previous research has implemented the VaR, EVT, and portfolio diversification measures. However, in the research of Gilli and Këllezi (2006), the application of the EVT method is carried out for several markets but only for one form of risk, namely daily returns. Then, the research of Esterhuysen et al. (2008) focused on the data of several operational risks but only used VaR without implementing EVT. Meanwhile, operational risks are generally large in number but rarely by occurrence or vice versa. Therefore, it is worth implementing the EVT because of these operational risk characteristics. Yao et al. (2013) realized the importance of EVT for measuring operational risk. However, the processing of some risks was carried out through data grouping. This data grouping method cannot be representative of several types of risk that are measured directly. Another method is needed to represent the weight of each risk, one of which is the portfolio approach. van Schalkwyk and Witbooi (2017) carried out a portfolio approach to determine the allocation strategy in risk management. However, risk measurement is based on stochastic modeling. Stochastic modeling is not suitable for measuring operational risk due to specific characteristics. Therefore, Table 1shows the gap between previous studies and the current research. Previous studies did not measure EVaR based on multiple risks with a portfolio approach, as this study has. In addition, there has been no previous research that uses digital banking transaction risk data as this study has. Based on the research gap, this study intends to determine the maximum potential loss for the operational risk of digital banking transactions using the extreme value-at-risk (EVaR) method. The EVaR method is thought to be able to accurately measure risk for extreme events of digital banking risk loss. This is due to the extreme modeling approach suited to operational risk characteristics of digital banking as an extreme event (Abbate et al. 2009). This study promotes advantages over other studies because it performs EVaR analysis based on a combination of risk with a portfolio approach. The EVaR results represent several risks at once. This research’s contribution is to provide banks with advice and materials for consideration and evaluation in digital transaction risk management activities. The results of this study can be used as material for calculating the allocation of operational risk reserve funds to avoid collapse due to potential losses. 2. Literature Overview 2.1. Digital Banking Transaction Digital banking is the transformation of all traditional banking activities and services into a digital environment. Digital banking is one of the bank services that allows customers to obtain information, communicate, and conduct banking transactions through the internet service network. In general, digital banking is an operating model based on a technology platform for exchanging information and conducting transactions between banks and customers. This process is carried out through digital devices connected to computer software in an internet environment (Mbama et al. 2018). Digital banking transactions have two types of services based on the platform, namely web, and mobile platforms. The web platform can be used with a computer via a browser. As for the mobile platform, it is only used with mobile phones through digital banking applications (He 2015). Digital technology provides benefits to customers (Dinçer et al. 2021). For customers, banking provides transactions that are convenient in terms of time, place, and cost. Customers do not need to visit the bank office to obtain information or perform banking transactions. As a result, the use of digital banking makes it easier and faster for customers to make financial transactions. For banking companies, digital banking services increase fee-based income and reduce operational costs when compared to transaction services through relatively large branch offices, which require the bank to pay employees, building rent, security, electricity, and others. The financial transactions include purchases, transfers, payments, and so on (Yoon and Steege 2013;Jang-Jaccard and Nepal 2014). Therefore, cash transactions can actually disappear, and payments can be centered on digital platforms (Mikhaylov 2021). Risks 2022,10, 10 5 of 18 2.2. Digital Banking Transaction Risks Digital banking transaction risk includes the risk that occurs due to the failure of a system in digital financial transactions. Some of the risks that may occur include the threat of cyber-attacks, errors from system users, possible defects of the internet system or applications used, or service downtime due to system failures on the application side. Digital banking risks will have a negative impact on companies if mitigation is not carried out. Banking risks can negatively affect the company’s business in the following ways: (a) decrease the level of market confidence and business players; (b) decrease the level of investor confidence; (c) decrease the company’s value; (d) decrease or lose the business’ competitive value; and (e) potentially lead to lost income (Sathyanarayana 2014). The possible risk of digital financial transaction activities in banking can be observed from the operational risk perspective. Operational risk is caused by errors in the operation of a system and includes both internal and external factors. In this context, the provision of digital financial transaction services has potential losses arising from operational risks (Ferreira and Dickason-Koekemoer 2019). 2.3. Operational Risk Churchill (2013) revealed that risk is divided into pure and speculative risks. Speculative risk is further divided into four types of risk, namely market risk, credit risk, liquidity risk, and operational risk. The Basel framework defines operational risk as the risk of loss resulting from inadequate or failed internal processes, people and systems, or external events. In other words, operational risk can come from processes, structures, systems, and internal or external factors. This study focuses on operational risks originating from the system, namely potential losses from digital transaction risks due to downtime and service timeouts. This study focuses on the risks associated with downtime and timeout because these risks are the most common in the digital banking system. This is based on the system’s need for maintenance in a period that causes downtime. In addition, connection problems often occur and interfere with transactions. If this occurs, the system will timeout because the system loading exceeds the service level agreement time (AlAbdullah et al. 2010). One of the steps in mitigating risk is recognizing the risks, which is known as risk identification. Risk identification is an initial action that provides input to measure, monitor, and control these risks. The better the risk identification action, the better risk mitigation will be. The result of the required risk identification process is a risk measure. Risk measures are useful for risk mitigation because banking companies already know how the impact of risks may occur. Based on these risk measures, companies can take strategic steps to carry out risk management (Churchill 2013). 2.4. Measurement of Operational Risk Based on the Basel Standard Efficient operational risk management will ultimately improve the company’s business performance in general. On the other hand, the inability to manage operational risk will make the company suffer losses and then will have an impact on the company’s capital. If the company’s business capital is getting smaller, then the company’s sustainability is not optimal. Operational risk management is based on the measurement of operational risk loss itself. There is a standard method for measuring operational risk losses in the Basel Committee on Banking Supervision (Basel II). The standard measurement method promotes three approaches in measuring operational risk losses. The three approaches use different risk exposure indicators, namely: (a) the basic indicator approach (BIA), (b) the standardized approach (SA), and (c) the advanced measurement approach (AMA) (Hubbert 2012). AMA measures operational risk with internal methods. The internal model consists of assumptions, statistical techniques, key performance indicators, and other mathematical and economic techniques. The process of collecting internal data affects the relevance, quality, and standardization of content. The basic difference between AMA and BIA or SA is the parameter of the probability of the event being considered. The BIA and SA methods Risks 2022,10, 10 6 of 18 only consider the average gross profit in determining risk measures, whereas the AMA considers data on losses that have occurred and the probability of risk events. Therefore, the AMA method will be more powerful in identifying risks. The internal approaches are grouped as the AMA model and include the following: the internal measurement approach (IMA), the bootstrapping approach, the loss distribution approach (LDA), the Bayesian approach, and the extreme value theory (EVT) (Hubbert 2012). This study uses a risk measurement technique with the EVT method. 3. Materials and Methods Materials are data objects and software used in a study, whereas the method comprises models used in analyzing the data. The descriptions of the materials and methods in this study are sequentially explained below. 3.1. Materials This research uses digital banking transaction risk data due to downtime services and service timeouts. The nominal risk loss data is obtained by simulating the risk data sample at one of the commercial banks in Indonesia. As for the initial sample data, it represents the risk of digital banking losses due to downtime and timeouts. The sample data period is 1 May 2020 to 31 August 2020. Then, the sample data becomes material for digital banking risk simulation. Banking companies as a sample cannot be mentioned because they are protected by Law No. 30/2000. The law regulates company secrets, including information in technology and business. Confidential company information is an asset that has economic value and is not known by the public (Government of Indonesia 2000). The characteristics of these banking companies are in the BUKU IV bank group. Based on the Indonesian Financial Services Authority Regulation (6/POJK.03/2016), BUKU IV is a bank with the highest core capital of at least IDR30,000,000,000. 3.2. Methods The methods used in this study are maximum entropy bootstrapping (MEBoot), the threshold percentage method, the peak-over-threshold method, generalized Pareto distribution, the extreme value theory, and extreme value-at-risk (EVaR). In addition, this study uses several software to process the data, namely R software, Excel, and EasyFit. 3.2.1. Maximum Entropy Bootstrapping (MEBoot) Bootstrapping was first introduced as a method for resampling data by Efron (Efron 1982) in 1982. It is used as a solution to the problem of outliers in statistics. It can also be used to estimate the sampling distribution by surrogate sampling from the original sample to obtain the parameter’s confidence level. In addition, it is the resampling of data with random depiction by replacing a series of data points so that data distribution can be close to normal. Later, Vinod and López-de-Lacalle (2009) developed a bootstrap based on the principle of maximum entropy, commonly called MEBoot. MEBoot is a method for obtaining robust estimates of standard errors and confidence intervals as estimates of proportion, mean, median, odds ratio, correlation coefficient, or regression coefficient. The MEBoot algorithm is simplified from the original version for practical reasons. The MEBoot algorithm can be decomposed into six steps: (1) sort the original xt data so that they are arranged from the smallest to the highest; (2) calculate intermediate points zt=x(t)+x(t+1) 2 ; (3) calculate the trimmed mean, mtrim , of the deviation xt−xt−1 for any two consecutive data sets; then, count the left tail z0=x(1)−mtrim and the right tail zT=x(t)−mtrim ; (4) generate a uniform random number (0, 1) of some original data xt and sort and count the quantile samples for each U (0, 1); (5) reorder the obtained quantiles according to the order index vectors recorded in the steps to recover the dependent relationship on the original observation data; and (6) repeat steps 1–5 repeatedly until the desired repeat size. Risks 2022,10, 10 7 of 18 In this research, MEBoot uses R software (MEBoot package) to facilitate data management. The command function used is MEBoot (x, reps, trim = list (trim = 0.10), reachbnd = TRUE, expand.sd = FALSE, force.clt = TRUE, scl.adjustment = TRUE). 3.2.2. Threshold The threshold is a lower limit value from the tail of the distribution that fits the extreme value distribution. The determination of the threshold value is seeking the optimal balance to obtain model errors and parameter errors to a minimum. One of the methods to determine the threshold is the percentage method, which is more practical and easier to implement. This study uses the percentage method for the determination of the threshold. Based on extensive research simulation, Rydman (2008) recommended choosing the threshold such that the data above the threshold value is approximately 10% of the total data. The data above the threshold value is called extreme data. Lots of extreme data is obtained using this equation: m=10% ×n, (1) where mis lots of extreme data and nis lots of total observed data. Then, the threshold value uis obtained using this equation: u=m+1, (2) 3.2.3. Extreme Value Theory (EVT) EVT is a branch of statistics that discusses data deviations from the mean in the probability density function. EVT is generally used in extreme data modeling, such as rare loss events, but has a big impact. The usual approach cannot model the arising losses. The probability of extreme events is difficult to identify because of the lack of data held in the modeling process. Therefore, the usual modeling approach cannot be applied (Gomes and Guillou 2015). There are two methods that can calculate the identification of extreme values from the data of loss value. The first method is the maxima block, which is the traditional method used to analyze seasonal data. Each block of the period is determined to be the maximum loss value. Second, the peaks-over-threshold (POT) method uses data more efficiently by identifying extreme values above a certain maximum loss value or threshold value (Ferreira and De Haan 2015). In this study, the peaks-over-threshold (POT) method is used to determine the extreme value. 3.2.4. Peaks-Over-Threshold (POT) The POT method identifies extreme values by setting the threshold values and ignoring the time of occurrence. Extreme values are data that are above the threshold value. This extreme value becomes the distribution model. The POT method applies the Pickland– Balkema–de Haan theorem, which states that the higher the threshold, the more the data distribution above the threshold will follow the generalized Pareto distribution (GPD) (Makarov 2007). The assumption of data above the threshold that follows the GPD is obtained by looking at the tail of the distribution away from the trust line. A heavy tail can be detected by making a QQ plot against data above the threshold. Risks 2022,10, 10 8 of 18 3.2.5. Generalized Pareto Distribution (GPD) GPD is defined as the distribution limit of scaled excesses above the threshold value. Supposing xis a random variable from loss risk with two GPD parameters, the GPD distribution function of xis as follows (Baran and Witzany 2011). gξ,β(x)=     1 β1+ξ βx−1−1 ξ,ξ6=0 1 βexp−x β,ξ=0 , (3) where β > 0; x ≥ 0 if ξ > 0; 0 ≤x≤ − β ξ if ξ < 0, with ξ indicating the shape parameter and βindicating the scale parameter. The GPD can be divided into three types based on the shape parameter value ( ξ ) as follows: exponential distribution if the value ξ = 0, Pareto type I distribution if ξ > 0, and Pareto type II distribution if ξ < 0 (Baran and Witzany 2011). Zhao et al. (2019) discussed the estimation of generalized Pareto parameters. The formula of parameter estimation is obtained by the maximum likelihood estimation (MLE) method. This study estimates GPD parameters with the help of EasyFit software with fit distribution tools. 3.2.6. Extreme Value-at-Risk (EVaR) Method Extreme value-at-risk (EVaR) measures losses arising from extreme risk with a certain confidence level. The risk measure is started based on the excess loss function. Suppose Xis a random variable (Mwamba et al. 2017), the conditional distribution function Fu of excess losses above the threshold uis defined as Fu(y)=P[X−u≤y|X>u], (4) to 0 ≤y≤XF−u , XF is its least upper bound of F. Where XF=Sup{x∈R:F(x)<1}≤ ∞and y=x−uis the excess above u. Equation (4) can be written in the form Fu(y)=P[X−u≤y,X>u] P[X>u]=P[u<X≤u+y] 1−P[X≤u]=F(u+y)−F(u) 1−F(u)=F(x)−F(u) 1−F(u), (5) the parametric model of the distribution function’s excess loss Fu of the generalized Pareto distribution (GPD) is based on the limit theorem, i.e., the Picklands–Balkema–de Haan theorem (Kang and Song 2017;Jockovi´c 2012). It is based on the Picklands–Balkema–de Haan theorem where ularge and approaching XF, where β(u) is a positive real function. lim u→XF Sup 0≤y≤XF−u |Fu(y)−Gξ,β(u)(x−u)|=0, (6) so that the excess loss function of Fu converges to GPD Gξ,β and can be written as Fu(x)= Gξ,β(x−u). Then, the result of Equation (5) substituted to the underlying distribution function (x) of Equation (6) can be written as F(x)=(1−F(u))Gξ,β(x−u)+F(u), (7) where n is the sample size of the data and Nu represents the number of losses above the threshold u. The estimator tail of F(x) for x>uis ˆ F(x)=Nu n 1−1+ξ(x−u) β−1 ξ!+1−Nu n ˆ F(x)=1−Nu n1+ξ(x−u) β−1 ξ, (8) Risks 2022,10, 10 15 of 18 of Basel III risk-based capital regulations in Indonesia, there are things that the OJK must consider. The first thing is that the explanation of indicators in calculating gross income for the BIA method is not explicitly specified in the regulations. Furthermore, OJK needs to describe the scope of operational risk that is clearer and consistent with Basel standards. In addition, OJK does not implement the AMA method for measuring operational risk (Bank for International Settlements 2016). This is unfortunate because the BIA method is a very simple traditional approach compared to the AMA. The AMA method demands that banks use internal loss data to calculate the EVaR of operational risk. The size of the operational loss will be in line with the state of risk in the banking company. If the banking company has implemented operational risk prevention well, then the value of the potential loss is lower. This is related to historical data on operational risk losses from the company. However, this is not the case with the BIA method, which is not influenced by a strong operational risk management environment. The results of this study provide a comparison of the measurement of operational risk between the AMA and BIA methods. The BIA method measures operational risk capital requirements based only on gross income from the bank, so it is not sensitive to operational risk. The BIA formula is risk capital =Gross income ×β , with β= 15%. The BIA formula is very simple when compared to the EvaR formula in Equation (10). BIA, which uses gross income as an indicator of operational risk exposure, can be categorized as a traditional measure. Meanwhile, the maximum potential loss value with EVaR is included in the advanced measurement approach (AMA). EVaR performs an operational risk assessment based on the distribution of loss data. This adds to the security of operational risk estimates. The results obtained in the AMA method tend to be smaller than the BIA method (Zhu et al. 2019). Smaller yields can be leveraged for the minimum optimal backup value. The minimum optimal reserve fund will make capital diversification better. The remaining excess capital can be used for the company’s investment interests. Thus, banking companies can have more sources of income. On the other hand, one of the most visible impacts of implementing EVaR in the AMA approach to operational risk management is the positive impact on reputation and stakeholder perceptions. A better risk calculation process certainly provides shareholders, clients, rating agencies, and the market with clear information on safety risk management. This certainty is very important and provides comfort for stakeholders, especially in times of economic turmoil and uncertainty. Therefore, this is a very useful approach for the sustainability of the company that is safe against risk, especially when it comes to the operational system of digital banking. 6. Conclusions This study discusses the analysis of the maximum potential loss from digital banking transactions. The analysis result shows the maximum potential loss from the risk of digital banking transactions is IDR144,357,528,750.94 with a 95% confidence level. The extreme value-at-risk (EVaR) method used in this study uses the generalized Pareto distribution (GPD) method. The GPD is interpreted as a distribution that describes extreme data. Digital banking risk is an extreme risk. Therefore, the analysis results of this study are in accordance with the characteristics of the risk. Thus, the result of the maximum potential loss value becomes a reference for mitigating digital banking risk. Banking companies need to provide reserve funds that can cover these potential losses. If banks cannot provide these reserve funds, it is feared that a collapse will occur. In particular, unexpected extreme events such as a global financial crisis can occur at any time. If this occurs, the unpreparedness of reserve funds can certainly make the bank company collapse. Therefore, the potential for maximum loss is an important concern for risk mitigation efforts. This study still has limitations related to the exploration of digital banking risk data. For further studies, attention can be paid to more types of digital banking risks, one of which is the risk of digital banking from the customer’s point of view as a user. There are digital banking risks that arise from users, such as transaction errors. In addition, Risks 2022,10, 10 16 of 18 the leakage of customer account data is also a calculated risk. The leakage of customer account data can be misused by irresponsible parties. The misuse of customer data can harm banking companies, so data security also needs to be a risk management concern. Therefore, further research can explore digital banking risks. Risk exploration is expected to strengthen the estimated loss, and better loss estimation will make risk management safer. Author Contributions: Conceptualization, M.P.A.S. and S.; methodology, M.P.A.S. and S.; software, M.P.A.S. and D.C.; validation, M.P.A.S., S. and D.C.; formal analysis, S.; investigation, D.C.; resources, S.; data curation, M.P.A.S.; writing—original draft preparation, M.P.A.S.; writing—review and editing, S.; visualization, M.P.A.S. and D.C.; supervision, S.; project administration, M.P.A.S. and S.; funding acquisition, S. All authors have read and agreed to the published version of the manuscript. Funding: The APC was funded by Universitas Padjadjaran. Institutional Review Board Statement: Ethical institutional review and approval were waived for this study due to neither institution nor government were involved. In this study, used simulation of the open-access data sample. This is also following the regulations of Law Number 14 of 2008 concerning the openness of public information (https://jdih.esdm.go.id/storage/document/UU%20 No.%2014%20Thn%202008.pdf, accessed on 25 October 2021). Data Availability Statement: Data is contained within the article. Acknowledgments: The authors are grateful to the constructive comments from four anonymous reviewers. The author would also like to thank the Directorate of Research and Community Service (DRPM) of Universitas Padjadjaran. Conflicts of Interest: The authors declare no conflict of interest. References Abbate, Donato, Elise Gourier, and Walter Farkas. 2009. Operational risk quantification using extreme value theory and copulas: From theory to practice. The Journal of Operational Risk 4: 1–24. [CrossRef] Aebi, Vincent, Gabriele Sabato, and Markus Schmid. 2012. Risk Management, Corporate Governance, and Bank Performance in the Financial Crisis. Journal of Banking & Finance 36: 3213–26. AlAbdullah, Fadhel, Fahad H. Alshammari, Rami Alnaqeib, Hamid A. Jalab, Aos. A. Zaidan, and Bahaa. B. Zaidan. 2010. Analytical Study on Internet Banking System. Journal of Computing 2: 140–46. Bank for International Settlements. 2016. Regulatory Consistency Assessment Programme (RCAP)—Assessment of Basel III Risk-Based Capital Regulations—Indonesia. Basel: The BIS Media. Available online: https://www.bis.org/bcbs/publ/d394.pdf (accessed on 20 October 2021). Bank Indonesia. 2020. Annual Report Bank Indonesia. Available online: https://www.bi.go.id/id/publikasi/laporan/Documents/ Laporan_Keuangan_Tahunan_BI_Tahun-2020.pdf (accessed on 15 October 2021). Baran, Jaroslav, and Jiri Witzany. 2011. A Comparison of EVT and Standard VaR Estimations. Bulletin of the Czech Econometric Society 19: 1–27. Available online: http://ces.utia.cas.cz/bulletin/index.php/bulletin/article/view/185 (accessed on 15 October 2021). [CrossRef] Beccalli, Elena. 2007. Does IT investment improve bank performance? Evidence from Europe. Journal of Banking & Finance 31: 2205–30. Belás, Jaroslav, Michal Korauš, Felix Kombo, and Antonín Korauš. 2016. Electronic Banking Security and Customer Satisfaction Incommercial Banks. Journal Security Sustainable 5: 411–22. Boudt, Kris, Peter Carl, and Brian G. Peterson. 2013. Asset allocation with conditional value-at-risk budgets. The Journal of Risk 15: 39–68. [CrossRef] BRI. 2020. Annual Report BRI. Available online: https://bri.co.id/documents/20123/56786/Annual%20Report%20BRI%202020%2 0ver%20Indonesia.pdf (accessed on 12 October 2021). Carbo-Valverde, Santiago, Pedro Cuadros-Solas, and Francisco Rodríguez-Fernández. 2020a. A Machine Learning Approach to the Digitalization of Bank Customers: Evidence from Random and Causal Forests. PLoS ONE 15: e0240362. [CrossRef] Carbo-Valverde, Santiago, Pedro J. Cuadros-Solas, and Francisco Rodríguez-Fernández. 2020b. The Effect of Banks’ IT Investments on the Digitalization of their Customers. Global Policy 11: 9–17. [CrossRef] Casaló, Luis V., Carlos Flavián, and Miguel Guinalíu. 2007. The Role of Security, Privacy, Usability and Reputation in the Development of Online Banking. Online Information Review 31: 583–603. [CrossRef] Churchill, Craig Farren. 2013. Making Insurance Work for Microfinance Institutions: A Technical Guide to Develop and to Deliver Microinsurance. Geneva: International Labour Organization. Cividino, Sirio, Gianluca Egidi, Ilaria Zambon, and Andrea Colantoni. 2019. Evaluating the Degree of Uncertainty of Research Activities in Industry 4.0. Future Internet 11: 196. [CrossRef] Risks 2022,10, 10 17 of 18 Dinçer, Hasan, Anton Lisin, Gözde Gülseven Ubay, and Ça˘gatay Ça˘glayan. 2021. Identifying the Best Financing Sources for Renewable Energy Companies in Latin American Countries. Contributions to Management Science Book Series. Cham: Springer. [CrossRef] DTCC. 2017. DTCC Systemic Risk Barometer 2017 Q1. Available online: https://www.dtcc.com/news/2017/may/22/dtcc-systemicrisk-barometer-survey-reveals-increased-concerns-over-cyber-risk (accessed on 30 September 2021). Efron, Bradley. 1982. The Jacknife, the Bootstrap and Other Resampling Plans. Stanford: National Science Foundation, Division of Biostatistics. Esterhuysen, Jánel, Paul Styger, and Gary Van Vuuren. 2008. Calculating Operational Value-at-Risk in a Retail Bank. South Adrican Journal of Economic and Management Sciences 11: 1–16. [CrossRef] Ferreira, Suné, and Zandri Dickason-Koekemoer. 2019. A conceptual model of operational risk events in the banking sector. Cogent Economics & Finance 7: 1706394. [CrossRef] Ferreira, Ana, and Laurens De Haan. 2015. On the block maxima method in extreme value theory: PWM estimators. The Annals of Statistics 43: 276–98. [CrossRef] Gambrah, Priscilla Serwaa Nkyira, and Traian Adrian Pirvu. 2014. Risk Measures and Portfolio Optimization. Journal of Risk and Financial Management 7: 113–29. [CrossRef] Gilli, Manfred, and Evis Këllezi. 2006. An Application of Extreme Value Theory for Measuring Financial Risk. Society for Computational Economics 27: 207–28. [CrossRef] Gomes, M. Ivette, and Armelle Guillou. 2015. Extreme Value Theory and Statistics of Univariate Extremes: A Review. International Statistical Review 83: 263–292. Available online: https://onlinelibrary.wiley.com/doi/abs/10.1111/insr.12058 (accessed on 5 October 2021). [CrossRef] Government of Indonesia. 2000. Law No. 30. Available online: https://peraturan.bpk.go.id/Home/Details/45002 (accessed on 27 September 2021). He, Zhaozhao. 2015. Rivalry, Market Structure and Innovation: The Case of Mobile Banking. Review of Industrial Organization 47: 219–42. [CrossRef] Hernández-Murillo, Rubén, Gerard Llobet, and Roberto Fuentes. 2010. Strategic Online Banking Adoption. Journal of Banking & Finance 34: 1650–63. Hubbert, Simon. 2012. Essential Mathematics for Market Risk Management. Hoboken: John Wiley & Sons Ltd. Iman, Shrestha. 2020. Changes in Technological Payment Systems in Banking Sector of India. International Journal of Advanced Science and Technology 29: 2911–21. Available online: http://sersc.org/journals/index.php/IJAST/article/view/22976 (accessed on 2 October 2021). Institute of International Finance. 2017. The Future of Risk Management in the Digital Era. McKinsey & Company Report. Washington, DC: Institute of International Finance. Jang-Jaccard, Julian, and Surya Nepal. 2014. A survey of emerging threats in cybersecurity. Journal of Computer and System Sciences 80: 973–93. [CrossRef] Jockovi´c, Jelena. 2012. Quantile estimation for the generalized pareto distribution with application to finance. Yugoslav Journal of Operations Research 22: 297–311. [CrossRef] Kang, Suyeon, and Jongwoo Song. 2017. Parameter and quantile estimation for the generalized Pareto distribution in peaks over threshold framework. Journal of the Korean Statistical Society 46: 487–501. [CrossRef] Keister, Todd, and James McAndrews. 2009. Why Are Banks Holding So Many Excess Reserves? Federal Reserve Bank of New York Staff Reports, No. 380. New York: Federal Reserve Bank of New York. Lubis, Alexander, Constantinos Alexiou, and Joseph G. Nellis. 2019. Payment System Innovations and Financial Intermediation: The Case Of Indonesia. ADBI (Asian Development Bank Institute) Working Paper Series. Tokyo: ADBI. Makarov, Mikhail. 2007. Applications of exact extreme value theorem. The Journal of Operational Risk 2: 115–20. Available online: https://evmtech.com/wp-content/uploads/2013/02/Exact-EVT.pdf (accessed on 5 October 2021). [CrossRef] Mbama, Cajetan Ikechukwu, Patrick Ezepue, Lyuba Alboul, and Martin Beer. 2018. Digital banking, customer experience and financial performance. Journal of Research in Interactive Marketing 12: 432–51. [CrossRef] Mikhaylov, Alexey Yu. 2021. Development of Friedrich von Hayek’s theory of private money and economic implications for digital currencies. Terra Economicus 19: 53–62. [CrossRef] Mishra, Mayank. 2020. Evolution of the Invisible bank: How Partnerships with FinTechs Are Driving Digital Innovation. Journal of Digital Banking 5: 36–40. Available online: https://hstalks.com/article/5804/evolution-of-the-invisible-bank-how-partnershipsw/ (accessed on 2 October 2021). Muteba Mwamba, John, and Isaah Mhlanga. 2013. Extreme Conditional Value at Risk: A Coherent Scenario for Risk Management. München: Munich Personal RePEc Archive. Mwamba, John W. Muteba, Shawkat Hammoudeh, and Rangan Gupta. 2017. Financial tail risks in conventional and Islamic stock markets: A comparative analysis. Pacific-Basin Finance Journal 42: 60–82. [CrossRef] Nethravathi, Rao, Periyapatna Sathyanarayana, Gokarna Vidya Bai, Cristi Spulbar, Mendon Suhan, Ramona Birau, Toni Calugaru, Iqbal Thonse Hawaldar, and Abdullah Ejaz. 2020. Business intelligence appraisal based on customer behaviour profile by using hobby based opinion mining in India: A case study. Economic Research-Ekonomska Istraživanja 33: 1889–908. [CrossRef] Ojeniyi, Joseph A., Elizabeth O. Edward, and Shafii M. Abdulhamid. 2019. Security Risk Analysis in Online Banking Transactions: Using Diamond Bank as a Case Study. International Journal of Education and Management Engineering 9: 1–14. [CrossRef] Risks 2022,10, 10 18 of 18 Ortiz, Roberto, Mauricio Contreras, and Cristhian Mellado. 2021. Improving the volatility of the optimal weights of the Markowitz model. Economic Research-Ekonomska Istraživanja, 1–23. [CrossRef] Rahman, Ashiqur, Zoltan Rozsa, and Martin Cepel. 2018. Trade Credit and Bank Finance—Evidence from the Visegrad Group. Journal of Competitiveness 10: 132–48. [CrossRef] Rydman, Max. 2008. Application of the Peaks-Over-Threshold Method on Insurance Data. Project Report. Uppsala: Uppsala University. Sarma, Gunajit, and Pranav Kumar Singh. 2010. Internet Banking: Risk Analysis and Applicability of Biometric Technology for Authentication. International Journal of Pure and Applied Sciences and Technology 1: 67–78. Sathyanarayana. 2014. Risk Management in E-Banking Sector—An Analytical Study. European Scientific Journal 1: 357–60. Available online: https://eujournal.org/index.php/esj/article/view/4104/3937 (accessed on 15 October 2021). Survey on Financial Inclusion and Access (SOFIA). 2017. Understanding ‘People’s Use of Financial Services in Indonesia; Jakarta: Indonesian Ministry of National Development Planning (BAPPENAS). Available online: https://www.bappenas.go.id/files/6415/1668/26 23/SOFIA_Report_May_2017_low_res.pdf (accessed on 18 October 2021). Susanto, Aries, Younghoon Chang, and Youngwook Ha. 2016. Determinants of Continuance Intention to Use the Smartphone Banking Services: An Extension to the Expectation-Confirmation Model. Industrial Management and Data Systems 116: 508–52. Available online: https://www.cjournal.cz/files/300.pdf (accessed on 2 October 2021). [CrossRef] Tanase, Rare¸s D., and Răzvan Serbu. 2010. Operational Risk and E-Banking. Bulletin of the Transilvania University of Bra¸sov: Economic Sciences 3: 327. van Schalkwyk, Garth J., and Peter J. Witbooi. 2017. A Model for Bank Reserves Versus Treasuries under Basel III. Applied Stochastic Models in Business and Industry 33: 237–47. Vinod, Hrishikesh D., and Javier López-de-Lacalle. 2009. Maximum Entropy Bootstrap for Time Series: The MEBoot R Package. Journal of Statistical Software 29: 1–19. [CrossRef] Williams, R., J. D. Van Heerden, and W. J. Conradie. 2018. Value at Risk and Extreme Value Theory: Application To The Johannesburg Securities Exchange. Studies in Economics and Econometrics 42: 87–114. [CrossRef] Yanagawa, Eiichiro. 2020. Technology-driven Next-Gen Corporate Banking: Trends and Implications in APAC and Japan. Journal of Digital Banking 5: 61–82. Yao, Fengge, Hongmei Wen, and Jiaqi Luan. 2013. CVaR measurement and operational risk management in commercial banks according to the peak value method of extreme value theory. Mathematical and Computer Modelling 58: 15–27. [CrossRef] Yoon, Hyun Shik, and Linsey M. Barker Steege. 2013. Development of a quantitative model of the impact of customers’ personality and perceptions on Internet banking use. Computers in Human Behavior 29: 1133–41. [CrossRef] Zabala Aguayo, Francisco, and Beata ´ Slusarczyk. 2020. Risks of Banking Services’ Digitalization: The Practice of Diversification and Sustainable Development Goals. Sustainability 12: 4040. [CrossRef] Zhao, Xu, Zhongxian Zhang, Weihu Cheng, and Pengyue Zhang. 2019. A New Parameter Estimator for the Generalized Pareto Distribution under the Peaks over Threshold Framework. Mathematics 7: 406. [CrossRef] Zhu, Xiaoqian, Jianping Li, and Dengsheng Wu. 2019. Should the Advanced Measurement Approach for Operational Risk be Discarded? Evidence from the Chinese Banking Industry. Review of Pacific Basin Financial Markets and Policies 22: 1950007. [CrossRef]